IBPS PO Mains 30 Nov 2024 Shift 2 Paper

Concept:Use the profit and discount relation to find the cost price, then apply the forecast-to-cost ratio and compare market price with forecast price to decide demand.Explanation:Cost price of B in 2014 is the square of a 2-digit number from 12 to 15, so the possible values are:$$12^2 = 144,\quad 13^2 = 169,\quad 14^2 = 196,\quad 15^2 = 225$$After giving $D\%$ discount on the market price of ₹420, the selling price is:$$SP = 420\left(1 - \frac{D}{100}\right)$$Profit is 50% on cost price, so $SP = 1.5 \times CP$. Equating both expressions:$$1.5 \times CP = 420\left(1 - \frac{D}{100}\right) \Rightarrow CP = 280\left(1 - \frac{D}{100}\right)$$Testing the possible CP values, only $CP = 196$ gives an integer discount:$$196 = 280\left(1 - \frac{D}{100}\right) \Rightarrow D = 30$$So, cost price of B in 2014 is ₹196.Given forecast price : cost price $= 30 : 28$,$$\text{Forecast price (2014)} = \frac{30}{28} \times 196 = \text{Rs. }210$$Since market price ₹420 is greater than forecast price ₹210, demand is low in 2014, confirming the given condition.Forecast price for 2015 rises by 25%:$$\text{Forecast price (2015)} = 210 \times 1.25 = \text{Rs. }262.5$$The actual price of B in 2015 is ₹320, which is greater than the forecast price ₹262.5, so demand remains low.Answer:Forecast price is ₹262.5 and demand is low. Hence, option A.